A problem is regarded as inherently difficult if solving the problem requires a large amount of resources, whatever the algorithm used for solving it.

What is a more elegant, and perhaps more correct, way of expressing the notion “a large amount of ” in a context like this?

EDIT after comments: Maybe what bothers me is the the large amount followed by plural resources. I like a large amount of butter on my morning toast; and I like having a lot of books around; but I’m not so sure I’d say I like having a large amount of books here.

FINALLY I changed the sentence to read

A problem is regarded as inherently
difficult if its solution
requires significant resources,
whatever the algorithm used.

I think "crapload" ought to be a standardized unit of measurement, e.g. "That truck can hold six craploads of concrete bricks!" (Brings a whole new meaning to shit bricks, no?)
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CycloneApr 17 '11 at 2:06

@Cyclone -- LOL! Although the notion "crapload" is infinitely expandable and might not admit of standardization.
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Pete WilsonApr 17 '11 at 12:45

“significant” doesn't imply that the amount is significant, though; only that there is some important significance of the resource. “Time is a significant resource” does not imply a large amount of time.
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bignoseMay 22 '14 at 5:16

Sure, if the word is singular as you use it. But when resources is plural, significant as a modifier usually refers to quantity.
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RobustoMay 22 '14 at 9:25

I think the right phrase here is a large number of resources. Amount should be used with a collective noun, such as a large amount of lumber. Number is used with a plural noun, such as a large number of boards.

I too dislike the phrase "a large amount of," whether followed by a singular or a plural noun. It's simply too wordy. I'd prefer "many" or "lots of" in most contexts, with "substantial" as an alternative in formal writing. One sturdy, straightforward source for this kind of phrase replacement is The Appropriate Word, by J.N. Hook (Addison-Wesley, 1990). http://books.google.com/books?id=JqFiAAAAMAAJ

If you think that's too wordy, get a large amount of this, from the blurb of the book (which I like; thanks for that and +1 to you): "A guide to proper usage for standard written, as well as conversational, English" How d'ya like them apples, bub? :-)
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Pete WilsonApr 17 '11 at 1:51

It seems the theory in question is concerned about the proportion of available computational resources available to devote to any one problem. In this context, disproportionate resources would work well. Since disproportionate could also mean too few, you may need to qualify it as a disproportionately large amount of resources, but I think the simpler phrase remains clear from the context.

I think OP is concerned with 'difficult' problems as (loosely) defined from the mathematical point of view, whereas disproportionate sounds more appropriate in a commercial software context. Pure mathematicians don't really care if their computing demands are disproportionate, so long as they can get access to sufficient processing power for whatever they're investigating.
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FumbleFingersApr 16 '11 at 16:28

@FumbleFingers: The OP link puts the quote in the context of a definition of computational complexity theory and an explanation of how it differs from analysis of algorithms and computability theory. My suggestion was in response to phrases I read there like quantifying the amount of resources, determine the practical limits, and appropriately restricted resources.
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CallithumpianApr 16 '11 at 17:01